We are interested in LRCs which can correct as many erasures as possible. The best one could hope for is a set of values for entries in \(H\)  (as shown in (REF )) which can correct any set of erasures a generic matrix of that form can (one way to define a generic \(H\)  is to assume every entry is algebraically independent of each other). We know that a set of erasures \(E\)  can be recovered from if and only if the subset of columns of \(H\)  corresponding to \(E\)  have full rank. Using this it can be shown that a generic \(H\)  can correct an additional \(h\)  erasures distributed across local groups on top of the `\(a\) ' erasures in each local group. LRCs which can correct all such erasure patterns are called Maximally Recoverable (MR) LRCs. Maximal recoverability was first introduced by [1]}, [2]} and extended to more general settings in [3]}. MR-LRCs were also studied earlier in [4]} where they are called Partial-MDS (Maximum Distance Separable) codes.
